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http://www.spinellis.gr/pubs/Breview/2003-CR-SeaShell/html/review.html This is an HTML rendering of a working paper draft that led to a publication. The publication should always be cited in preference to this draft using the following reference:
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Diomidis Spinellis
Athens University of Economics and Business
Hans Meinhardt
The Algorithmic Beauty of Sea Shells
Springer-Verlag, Berlin, 2003
235 pp., ISBN 3-540-44010-0
Although biological phenomena are guided at a microscopic level by the laws of physics, their scale and complexity rarely allow us to effectively apply analytic scientific reasoning to obtain predictive and prescriptive results. The formation of geometric patterns on the bodies of organisms is a topic with a long and venerable tradition of scientific investigation. Explaining the regular macroscopic structures that result from microscopic processes could enlighten us on more complex problems such as the formation of patterns in higher organisms during their embryonic development.
Hans Meinhardt, in a book that is at the same time both informative and visually astounding, uses relatively simple partial differential equations to provide an explanation of how the complex sea shell patterns could be formed through the interaction of different agents in a dynamic growth system. Meinhardt uses a few basic mechanisms such as the activator-inhibitor scheme, autocatalysis, traveling waves, enforced desynchronization, and enhancing, antagonistic, or extinguishing reactions to develop a mathematical theory that explains a very large number of complex patterns. He starts from simple relief-like patterns, extends the concepts to explain patterns involving wavy lines, crossings, and triangles, finishing with even more complicated patterns such as parallel and oblique rows of staggered dots, and lines with tongues. A separate contributed chapter deals with the equally interesting topic of shell models in three dimensions.
The scientific method employed in the book is based on assuming plausible simple chemical or biological models whose rigorous mathematical modeling derives the patterns actually observed. The results obtained with this method are impressive, but one should remember that the bulk of the work is based on abstract modeling and observation of frozen specimens. Nature could well employ completely different mechanisms for deriving the same results. Corroborating experimental evidence collected during the growth progress of the actual organisms could settle this question, and the author provides supporting references when these are available, yet the richness and complexity of the underlying theory cries for experiments and measurements precisely focused to support it. The text also leaves largely unanswered the questions of the utility of the patterns it examines and the evolutionary processes that could have resulted in the formation of the pattern-forming mechanisms.
The book is accompanied by a CD-ROM with the source code and executable version of simulation programs and animated graphs of their output. The source code in the form of BASIC programs, the MS-DOS executables and the animated GIF files could benefit from capitalizing on the processing power of modern hardware, the graphics capabilities of the accompanying displays, and the richness and portability of today's languages and data formats. Still, the technological simplicity of the CD-ROM offerings makes them accessible on a wide variety of hardware.
Although the book's beautiful pictures of tropic sea shells and accurate renditions of the corresponding mathematical functions would tempt us to leave it on a coffee table for our friends to marvel this would be a mistake. By reading and understanding how these humble organisms develop their amazingly beautiful patterns we are offered a rare opportunity to capture a glimpse of the inner working of the Nature's laboratory.
